Subgroups — C₅×Q₈⋊C₉ #67084

Order 360.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×Q₈	C₃	1	1	yes	maximal, characteristic
2	C₂×C₅×C₉	—	4	1	no	maximal
3	Q₈⋊C₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₄×C₅	—	3	1	no	—
5	C₅×C₉	—	4	1	no	Hall
6	C₅×Q₈	C₉	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₅	A₄	1	1	yes	characteristic
8	C₃×Q₈	C₃×C₅	1	1	yes	characteristic
9	C₄×C₅	—	3	1	no	—
10	C₂×C₉	—	4	1	no	—
11	C₃×C₅	SL(2,𝔽₃)	1	1	yes	characteristic
12	C₃×C₄	—	3	1	no	—
13	C₂×C₅	C₂²⋊C₉	1	1	yes	characteristic
14	C₉	—	4	1	no	Sylow
15	Q₈	C₅×C₉	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃	C₅×A₄	1	1	yes	characteristic
17	C₅	Q₈⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₄	—	3	1	no	—
19	C₃	C₅×SL(2,𝔽₃)	1	1	yes	characteristic
20	C₂	C₅×C₂²⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical, hypercenter	C₂×C₃×C₅	A₄
commutator, hypocenter	Q₈	C₅×C₉
Frattini	C₂×C₃	C₅×A₄
Fitting	C₃×C₅×Q₈	C₃
cosocle	C₃×Q₈	C₃×C₅
LCS	G ▷ Q₈
UCS	C₁ ◁ C₂×C₃×C₅

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.